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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the Atkin $U_t$-operator for $\Gamma _0(t)$-invariant Drinfeld cusp forms
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by Andrea Bandini and Maria Valentino PDF
Proc. Amer. Math. Soc. 147 (2019), 4171-4187 Request permission

Abstract:

We study the Atkin $U_t$ operator for Drinfeld cusp forms. In particular, we define newforms and oldforms of level $\Gamma _0(t)$ and we study basic properties of their slopes. Moreover, we find an explicit formula for the matrix associated to the action of $U_t$ on $\Gamma _1(t)$-invariant cusp forms using Teitelbaum’s interpretation as harmonic cocycles.
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Additional Information
  • Andrea Bandini
  • Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
  • MR Author ID: 660811
  • Email: andrea.bandini@unipi.it
  • Maria Valentino
  • Affiliation: Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università degli Studi di Parma, Parco Area delle Scienze, 53/A, 43124 Parma, Italy
  • MR Author ID: 1080348
  • Email: maria.valentino@unipr.it
  • Received by editor(s): July 4, 2018
  • Received by editor(s) in revised form: October 12, 2018, October 26, 2018, and November 29, 2018
  • Published electronically: June 27, 2019
  • Additional Notes: While this article was being written, the second author was supported first by an Outgoing Marie-Curie fellowship of INdAM and then by an “Ing. G. Schirillo” fellowship of INdAM
  • Communicated by: Matthew A. Papanikolas
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4171-4187
  • MSC (2010): Primary 11F52, 11F25; Secondary 20E08
  • DOI: https://doi.org/10.1090/proc/14491
  • MathSciNet review: 4002534